Thermal analysis of lid-driven porous pyramid enclosure subject to inclined magnetic field with heat source/sink and viscus effects: A parametric approach

This study presents a detailed numerical investigation of mixed convection within a porous, pyramidal cavity influenced by internal heat generation/absorption, viscous dissipation, and an inclined magnetic field. The physical model consists of a two-dimensional porous pyramid-shaped cavity with a centrally located circular obstacle acting as a heat source, where the bottom wall and obstacle are heated, the top wall is cooled, and the vertical sidewalls are adiabatic. The top and bottom walls move with equal and opposite velocities to induce lid-driven mixed convection, while isothermal heating/cooling and adiabatic sidewalls are imposed as thermal boundary conditions. The dimensionless governing equations were solved using the Galerkin finite element method in COMSOL Multiphysics. The fluid flow is modeled using the Darcy–Forchheimer porous medium formulation, incorporating viscous dissipation, and internal heat generation/absorption effects under an inclined magnetic field. Parametric analyses were conducted to examine the impact of key dimensionless numbers Darcy (Da), Richardson (Ri), Hartmann (Ha), heat generation/absorption (Q), Eckert (Ec), and Radiation (R) on flow structure and thermal transport. The results show that increasing Da enhances permeability, thereby intensifying convective mixing and heat transfer. Higher Ri values transition the flow from forced to natural convection, modifying streamline curvature and thermal layering. Stronger magnetic fields (Ha) dampen fluid motion, reducing the Nusselt number and distorting isotherms. Positive Q values elevate thermal gradients and circulation strength, whereas negative Q suppresses convective activity. Viscous dissipation (Ec) increases internal energy and temperature levels, complicating flow behavior. Radiation (R) flattens thermal profiles, lowering heat transfer efficiency. These findings provide valuable insights into heat transfer control within magneto-thermo-porous systems, with applications in thermal insulation, electronic cooling, and energy storage devices.